The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  X  1  1  1  1 X^2  1  1  1  0  1  1  1  X  1  1 X^2  1  0 X^2  1  0  1  1  1  1  0  X  X  1  0  1  X  0  1  0 X^2  0  0  1  X X^2 X^2  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2 X^2+X X^2+X X^2+X X^2  0  X  0  0 X^2+X  X X^2+X X^2  0  X  0  X X^2  0  0  0 X^2 X^2  X X^2+X X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2+X  0 X^2  X X^2+X  X  0 X^2  0  X  X X^2  0  X  0  0 X^2  X  0 X^2+X  X  X  X  0  X X^2  X X^2  X  X X^2  X  X  X  0  X  X X^2  X X^2+X  X  X  0  X  0  0  X  0 X^2
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2 X^2+X X^2 X^2+X  0  0  X X^2 X^2+X  X  X X^2+X  0 X^2  0 X^2  X  X  0 X^2+X  X  X  0  X  X  0  X  0 X^2+X  0 X^2+X  X X^2  X X^2 X^2  0  X X^2+X X^2+X  X X^2  0  X  X  X X^2+X X^2+X  X X^2+X  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2  0  0 X^2+X X^2+X X^2+X X^2  X  X  0 X^2+X X^2  X X^2  0  0 X^2  X  X X^2 X^2+X X^2+X  X  X
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+56x^87+102x^88+130x^89+103x^90+262x^91+148x^92+356x^93+69x^94+502x^95+126x^96+544x^97+96x^98+470x^99+121x^100+346x^101+56x^102+182x^103+82x^104+124x^105+39x^106+44x^107+36x^108+26x^109+11x^110+20x^111+17x^112+10x^113+8x^114+6x^116+2x^122+1x^148

The gray image is a linear code over GF(2) with n=388, k=12 and d=174.
This code was found by Heurico 1.16 in 33.1 seconds.